{"id":1313,"date":"2023-06-22T02:17:25","date_gmt":"2023-06-22T02:17:25","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypothesis-for-means-background-youll-need-2\/"},"modified":"2025-05-16T22:12:43","modified_gmt":"2025-05-16T22:12:43","slug":"null-and-alternative-hypothesis-for-means-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypothesis-for-means-background-youll-need-2\/","title":{"raw":"Module 12: Background You'll Need 2","rendered":"Module 12: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate mean and standard deviation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6531,&quot;3&quot;:{&quot;1&quot;:0},&quot;4&quot;:{&quot;1&quot;:2,&quot;2&quot;:16777215},&quot;10&quot;:2,&quot;11&quot;:4,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Calculate mean and standard deviation.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Recall that as we analyze the graph of a distribution of a quantitative variable, we pay attention to the overall pattern (shape, center, and spread), in addition to the data points that deviate from the overall pattern (outliers).<\/p>\r\n<p>Let's look at values that can be used as a measure of center and standard deviation as a measure of spread.<\/p>\r\n<section class=\"textbox recall\">The\u00a0<strong>mean<\/strong> of a data set is also commonly known as the average of a data set.<br \/>\r\n<br \/>\r\nThe\u00a0<strong>median<\/strong> of a data set is the middle value after all of the values have been arranged in ascending order.<br \/>\r\n<br \/>\r\n<strong>Standard deviation<\/strong> is the \u201ctypical\u201d distance of each data point from the mean of the data set.<\/section>\r\n<h4>Ages of Best Actress or Actor Winners from the Oscars<\/h4>\r\n<p>[latex]184[\/latex] observations of the ages of the Best Actress or Actor winners from movies from the Oscars awards ceremonies can be found listed under the data set <strong>Oscars: Age<\/strong> in the statistical tool below.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/ \" width=\"100%\" height=\"900\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]832[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate mean and standard deviation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:6531,&quot;3&quot;:{&quot;1&quot;:0},&quot;4&quot;:{&quot;1&quot;:2,&quot;2&quot;:16777215},&quot;10&quot;:2,&quot;11&quot;:4,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;}\">Calculate mean and standard deviation.<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Recall that as we analyze the graph of a distribution of a quantitative variable, we pay attention to the overall pattern (shape, center, and spread), in addition to the data points that deviate from the overall pattern (outliers).<\/p>\n<p>Let&#8217;s look at values that can be used as a measure of center and standard deviation as a measure of spread.<\/p>\n<section class=\"textbox recall\">The\u00a0<strong>mean<\/strong> of a data set is also commonly known as the average of a data set.<\/p>\n<p>The\u00a0<strong>median<\/strong> of a data set is the middle value after all of the values have been arranged in ascending order.<\/p>\n<p><strong>Standard deviation<\/strong> is the \u201ctypical\u201d distance of each data point from the mean of the data set.<\/section>\n<h4>Ages of Best Actress or Actor Winners from the Oscars<\/h4>\n<p>[latex]184[\/latex] observations of the ages of the Best Actress or Actor winners from movies from the Oscars awards ceremonies can be found listed under the data set <strong>Oscars: Age<\/strong> in the statistical tool below.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" width=\"100%\" height=\"900\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/eda_quantitative\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm832\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=832&theme=lumen&iframe_resize_id=ohm832&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1309,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1313"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1313\/revisions"}],"predecessor-version":[{"id":6802,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1313\/revisions\/6802"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1309"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1313\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1313"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1313"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1313"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}